Jim:
Thank you very very much for these quotes!
They provide a partial answer to my open query.
My chemical perspective from the early 21 Century follows.
Dear Ben, Gary R, Jerry--
Also in Vol 5 of the chronological edition (page 306 and 307)
Peirce speaks
of chemical valency:
BEGIN QUOTE
A straight road between two places, if not regarded itself as a
place, is
not a third place but only the pairedness of the two palces it
connects.
But a forking road involves a third place. Now no number of
straight roads
put end on end will ever have more than two ends after all; but
forking
roads put end on end with ramify into any number of ends. In like
manner,
in chemistry, were there no atoms but univalent ones, that is such
as are
capable fo pairing only, there could be no combination but binary
combinations. Whereas bivalent atoms, or those capable fo uniting
with two
others, which are therefore thirds, might give rise to combinations
of any
number of atoms. But bivalent atoms may be considered as involving
only
secondness in respect to having only two free bonds, and
consequently they
can only unite two univalent atoms however they may be arranged and
multiplied. While trivalent atoms because they have three free
bonds will
serve to unite any number of univalent atoms.
END QUOTe
I also find on page 393 of the same volume an entry in the Centruy
Dictionary for Element in which Peirce referes to the accepted
views of
Mendelejeff and himself (Peirce) provides a listing of 70 elements
arranged
in series and eight groups. I leave it to you folks to draw whatever
inferences you may -- nothing fruitful springs to my mind.
Cheers,
Jim Piat
A chemical interpretation of the quote can be given.
The first quote suggests that Peirce used a direct one to one
correspondence relation with the concept of valence as the principle
basis for his generalized logic.
This in turn suggests a simple bijective correspondence between the
concept of chemical valence values and firstness, secondness and
thirdness.
This is very, very surprising to me!
Remarkedly simple.
But how does this basis justify the generalization to a general
system of logic?
In particular:
If a valence of four had been known to Peirce, would he have
constructed a logic of firstness, secondness, thirdness and fourthness?
If a valence of five had been known to Peirce, would he have
constructed a logic of firstness, secondness, thirdness, fourthness
and fifthness?
If a valence of six had been known to Peirce, would he have
constructed a logic of firstness, secondness, thirdness, fourthness,
fifthness and sixthness?
If a valence of seven had been known to Peirce, would he have
constructed a logic of firstness, secondness, thirdness, fourthness,
fifthness, sixthness and seventhness?
And so forth.
The metaphor of length of combinations of paths with and without
branches is sort of a primitive precursor of the concept of
categories of mathematical graphs.
21 st Century chemistry has developed vastly richer concepts of valence.
Does this imply that 21 st Century chemistry is the potential basis
for a vastly richer logic? A "more general logic"? :-)
Is it not wonderful how a small number of facts can be abstracted
into beautifully constructed narratives that expand the domain of
discourse such the origins are fully and completely obscured?
Thanks again for posting the quote.
Cheers
Jerry LR Chandler
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